Question

two vectors undergo vector addition. vector a has a magnitude of 217 units and points to the north. vector b has a magnitude of 156 units and points to the west. what is the direction of the resultant vector? (the angle)

Answer 1

Explanation:

Given that,

The magnitude of vector A = 217 units to north

The magnitude of vector B = 156 units to west

Let R is the resultant. So,

$R=\sqrt{217^2+156^2} \\\\R=267.25\ \text{units}$

Let $\theta$ is the direction of the resultant vector. So,

$\tan\theta=\dfrac{y}{x}\\\\\tan\theta=\dfrac{217}{156}\\\\\theta=\tan^{-1}\left(\dfrac{217}{156}\right)\\\\\theta=54.28^{\circ}$

Hence, this is the required solution.